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63. Suspension Bridge Problem.  The following are the important features of a suspension bridge which should be considered in order to simplify the problem:
1.   The weights of the cables and of the chains are small compared with that of the road-bed.
2.   The road-bed is practically horizontal.
3.   The distribution of weight in the road-bed may be considered to be uniform.
We can, therefore, obtain a sufficiently close approximation if we consider an ideal bridge in which the cable and the chains have no weight and the distribution of weight in the road-bed is uniform in the horizontal direction. With these simplifications consider the forces acting upon that part of the cable which is between the lowest point and any point P, Fig. 41.
FIG. 41.
The forces are: The tensile force To, which acts horizontally at 0. The tensile force T, which acts along the tangent to the curve at P. The weight of that part of the bridge which is between 0 and P. If w be the weight per unit length of the road-bed and x denotes the length O'P', then the third force becomes wo;.
Therefore the conditions of equilibrium give
= 0; = -wx+Tsin 6= 0;
rcos0= To. T sin 0 = wx.